The Integration Methods tutor can be used to evaluate an integral step-by-step, using integration techniques discussed in class. You can either manually attempt different techniques on the integral, or let Maple decide which techniques to use. In some cases, Maple may find particularly clever substitutions and techniques that may not be immediately apparent when integration without software.
After opening the tutor, we begin by typing out the function and the variable name. For an indefinite integral, we leave the interval blank and click Start. When typing out the function in the tutor, you will not have access to the palettes toolbar in Maple, so you will need to type out commands such as sqrt() for square roots. You must also include the symbol * for multiplication.
If the Get Hint button is clicked, Maple will suggest an integration technique. In this case it gives a hint that there is multiplication in the integrand, so this is a good indication that we can apply the integration by parts formula:
\begin{equation*}
\int u \, dv = u v - \int v \, du\text{,}
\end{equation*}
where \(u=f(x)\) and \(v = g(x)\) are differentiable functions.
With this hint, we can click on the Parts button, where we will need to type in the functions for \(u=f(x)\) and \(v = g(x)\text{.}\) It is important to note that we do not type in the function for the differential \(dv\text{.}\) With these two functions input, we can click on Apply to see the result.
After opening the tutor, we begin by typing out the function, the variable name, and the interval. When typing out the function in the tutor, you will not have access to the palettes toolbar in Maple, so you will need to type out commands such as sqrt() for square roots. You must also include the symbol * for multiplication.
After clicking Start, we can see the integral and click on Next Step to see the integral evaluated one step at a time. Alternatively, we may click All Steps to see the entire process completed at once.
